Method of determining the engine charge temperature for fuel and spark control of an internal combustion engine

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to a method of determining the air temperature in the intake manifold of an internal combustion engine and, more particularly, to a method of defining a dynamic temperature model that predict the temperature of the air in the intake manifold of an internal combustion engine based on thermal transfer and vehicle parameters of the engine.

2. Discussion of the Related Art

Most internal combustion engines associated with a vehicle incorporate a temperature sensor positioned within the intake manifold of the engine to determine the temperature of the air entering the engine cylinders, sometimes referred to as the engine charge air temperature. This temperature measurement is important to provide the signals that control fuel and spark to the cylinders at the appropriate time for proper and efficient operation of the engine. Because colder air is more dense than hotter air, the amount of air charge in the cylinders is different depending on the charge air temperature, and thus the application of fuel and spark to the cylinders needs to vary depending on this temperature. In other words, the charge temperature is critical because this temperature determines the charge air quantity entering the cylinders regardless of the different ambient conditions. The charge temperature thus affects automatic idle speed (AIS), knock, start fuel and on-board diagnostics (OBD) features of the engine. Currently, a “speed-density” method is used for the fuel control. In combination with MAP and RPM readings, the charge temperature is used to determine the fuel injection pulse width control signal.

FIG. 1 depicts an engine control module <b>10</b> including a central processing unit (CPU) <b>12</b>. A number of sensor inputs are applied to the CPU <b>12</b>, and outputs from the engine control module <b>10</b> control certain operations of the vehicle engine, as is understood in the art. An ambient temperature measurement is currently provided to the engine control module <b>10</b> to control the engine radiator fan, A/C, exhaust gas recirculation (EGR), target idle speed, purge, O₂sensor diagnostics and start fuel controls. It has been determined that a relationship exists between the ambient air temperature and the charge temperature. However, current vehicles incorporate separate temperature sensors to measure both.

Temperature sensors are known, such as thermocouples, that can give highly accurate temperature measurements of the engine charge temperature. However, the type of temperature sensor generally positioned within the intake manifold is typically an inexpensive heat resistive element whose accuracy is limited.

What is needed is a technique for determining the charge temperature of the air in the intake manifold of an internal combustion vehicle that does not require a dedicated charge air temperature sensor, so as to eliminate the cost of the sensor and improve charge temperature accuracy. It is therefore an object of the present invention to provide such a technique.

SUMMARY OF THE INVENTION

In accordance with the teachings of the present invention, a non-linear, dynamic charge air temperature model is disclosed for determining the charge air temperature within an intake manifold of an internal combustion engine, where the charge air temperature model is based on the physical concepts of heat transfer and the system identification techniques. The charge air temperature model uses several available physical measurements from the vehicle, including inlet air temperature, engine coolant temperature, vehicle speed, manifold absolute pressure, engine speed, exhaust gas recirculation condition, and the engine radiator fan on/off state. The current charge air temperature is determined by the model at regular predetermined intervals from the physical measurements which are available in the engine systems, and the charge air temperature from the previous time. An estimation of an initial charge air temperature when the vehicle is initially turned on can be obtained based on the measurement of the engine coolant temperature and the inlet air temperature both at the time when the engine is turned off and at the time the engine is turned on, together with the estimated charge air temperature just before the engine is turned off.

Additional objects, advantages, and features of the present invention will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing the inputs and outputs of an engine control module;

FIG. 2 is a system view of a charge temperature prediction model, according to an embodiment of the present invention; and

FIG. 3 is an off-line procedure of model parameter calibration for the prediction module shown in FIG. <b>2</b>.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description of the preferred embodiments directed to a charge temperature prediction model for an internal combustion engine is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses. For example, the prediction model of the invention is specifically used for determining the charge air temperature of an internal combustion engine. However, the model may have uses in other areas for estimating or predicting temperature.

According to the present invention, a charge temperature prediction model has been developed based on the physical concepts of heat transfer and system identification technique to determine the charge temperature for a particular vehicle engine. Even though a physical relationship does exist between the ambient air temperature and the charge temperature, determination of the charge temperature is very complicated and affected by many engine operating conditions. In one embodiment, determination of the charge temperature T_mby the model is based on an inlet air temperature T_inmeasurement in combination with other already available engine data, including engine coolant temperature T_c, vehicle speed V_s, manifold pressure P, engine speed N, exhaust gas recirculation (EGR) condition, and the engine radiator fan on/off state V_f. As will be discussed below, these vehicle parameters, in combination with the physical concepts of heat transfer, will be used to estimate the charge temperature T_m.

First, it may be advantageous to develop a theoretical model of heat transfer that can be used to define the charge temperature model. The charge air temperature in the manifold is not only a heat transfer process but also a gas dynamic process. The basic governing equation of the temperature dynamics in the manifold is given by: <maths><math overflow="scroll"><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><mfrac><msub><mi>T</mi><mi>m</mi></msub><mrow><msub><mi>P</mi><mi>m</mi></msub><mo></mo><msub><mi>V</mi><mi>m</mi></msub></mrow></mfrac><mo>[</mo><mrow><mrow><msubsup><mi>a</mi><mi>a</mi><mn>2</mn></msubsup><mo></mo><mrow><msub><mi>m</mi><mi>ai</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mfrac><msub><mi>T</mi><mi>m</mi></msub><mrow><mi>γ</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><msub><mi>T</mi><mi>a</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><msubsup><mi>a</mi><mn>3</mn><mn>2</mn></msubsup><mo></mo><mrow><msub><mi>m</mi><mi>ci</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mfrac><msub><mi>T</mi><mi>m</mi></msub><mrow><mi>γ</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><msub><mi>T</mi><mi>e</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo></mrow></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><mrow><mrow><mrow><mo>(</mo><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo></mo><msub><mi>η</mi><mi>vol</mi></msub><mo></mo><msub><mi>P</mi><mi>m</mi></msub><mo></mo><mfrac><mi>ND</mi><mi>nx</mi></mfrac></mrow><mo>+</mo><mrow><mrow><msub><mi>hA</mi><mi>w</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mo>(</mo><mrow><msub><mi>T</mi><mi>mw</mi></msub><mo>-</mo><msub><mi>T</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mo>]</mo></mrow></mrow></mtd></mtr></mtable><mo></mo><mstyle>&lt;mtext /&gt;</mstyle><mo></mo><mi>where</mi><mo></mo><mstyle>&lt;mtext /&gt;</mstyle><mo></mo><mrow><msub><mi>m</mi><mi>ai</mi></msub><mo>=</mo><mrow><mfrac><mrow><msub><mi>A</mi><mi>t</mi></msub><mo></mo><msub><mi>C</mi><mi>D</mi></msub><mo></mo><msub><mi>P</mi><mi>a</mi></msub></mrow><msubsup><mi>a</mi><mi>a</mi><mn>2</mn></msubsup></mfrac><mo></mo><msup><mrow><msqrt><mfrac><mrow><mn>2</mn><mo></mo><mi>γ</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><msub><mi>C</mi><mi>p</mi></msub></mrow><mi>R</mi></mfrac></msqrt><mo></mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>-</mo><msup><msub><mi>X</mi><mn>1</mn></msub><mfrac><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow><mi>γ</mi></mfrac></msup></mrow><mo>]</mo></mrow></mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo></mo><msubsup><mi>X</mi><mn>1</mn><mfrac><mn>1</mn><mi>γ</mi></mfrac></msubsup></mrow></mrow><mo></mo><mstyle>&lt;mtext /&gt;</mstyle><mo></mo><mrow><msub><mi>m</mi><mi>ei</mi></msub><mo>=</mo><mrow><mfrac><mrow><msub><mi>A</mi><mi>e</mi></msub><mo></mo><msub><mi>C</mi><mi>De</mi></msub><mo></mo><msub><mi>P</mi><mi>e</mi></msub></mrow><msubsup><mi>a</mi><mi>e</mi><mn>2</mn></msubsup></mfrac><mo></mo><msup><mrow><msqrt><mfrac><mrow><mn>2</mn><mo></mo><mi>γ</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><msub><mi>C</mi><mi>p</mi></msub></mrow><mi>R</mi></mfrac></msqrt><mo></mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>-</mo><msup><msub><mi>X</mi><mn>1</mn></msub><mfrac><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow><mi>γ</mi></mfrac></msup></mrow><mo>]</mo></mrow></mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo></mo><msubsup><mi>X</mi><mn>1</mn><mfrac><mn>1</mn><mi>γ</mi></mfrac></msubsup></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr></mtable></math><img id="EMI-M00001" file="US06286366-20010911-M00001.TIF" img-content="math" img-format="tif" /><attachments><attachment idref="MATHEMATICA-00001" attachment-type="nb" file="US06286366-20010911-M00001.NB" /></attachments></maths>

where,

η_volis the engine volumatic efficiency;

N is the engine speed;

D is the engine displacement;

n is the number of cylinders;

x is the number of fire strokes in one revolution;

h is the heat transfer coefficient;

A is the surface area of the manifold;

γ is the ratio of specific heat;

a is the sound speed of gas;

t is the time;

C_Pis the constant pressure specific heat;

R is the gas constant; and

C_Dis the discharge coefficient.

Subscript:

a is the ambient air;

e is the exhaust gas;

m is the parameters in the manifold;

w is the parameters on the manifold wall; and

t is the parameters at throttle.

In equation (1), X is the pressure ratio across the throttle plate and the EGR valve, a is the speed of sound, X₁accounts for choked flow (X₁=0.528 if X&lt;0.528 and X₁=X if X&gt;0.0528), and T_mwis the mean manifold surface temperature. The equation defining T_mwmay be expressed as: <maths><math overflow="scroll"><mtable><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>mw</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mrow><mfrac><mrow><msub><mi>T</mi><mi>e</mi></msub><mo>-</mo><msub><mi>T</mi><mi>mw</mi></msub></mrow><msub><mi>R</mi><mi>c</mi></msub></mfrac><mo>+</mo><mfrac><mrow><msub><mi>T</mi><mi>a</mi></msub><mo>-</mo><msub><mi>T</mi><mi>mw</mi></msub></mrow><msub><mi>R</mi><mi>a</mi></msub></mfrac><mo>+</mo><mfrac><mrow><msub><mi>T</mi><mi>i</mi></msub><mo>-</mo><msub><mi>T</mi><mi>mw</mi></msub></mrow><msub><mi>R</mi><mi>f</mi></msub></mfrac><mo>+</mo><mfrac><mrow><msubsup><mi>T</mi><mi>c</mi><mn>4</mn></msubsup><mo>-</mo><msubsup><mi>T</mi><mi>mw</mi><mn>4</mn></msubsup></mrow><msub><mi>R</mi><mi>r</mi></msub></mfrac></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mtd></mtr></mtable></math><img id="EMI-M00002" file="US06286366-20010911-M00002.TIF" img-content="math" img-format="tif" /><attachments><attachment idref="MATHEMATICA-00002" attachment-type="nb" file="US06286366-20010911-M00002.NB" /></attachments></maths>

R_cis the heat conduction heat resistance, R_fmeans the forced convection heat resistance R_ais referred to as the natural convection heat resistance, and R_ris the radiation heat resistance.

These equations give an understanding to what physical variables the charge temperature is related to. However, these equations can not be used in the real time charge temperature prediction. First, the above equations require several inputs that are not available from the existing measurements in an engine control unit, such as the temperature and pressure of the ambient air and exhaust gas. Secondly, these equations contain many unknown nonlinear parameters and they are not easily determined or identified in a real application. Thirdly, the equations are mathematically complicated for a real time embedded system used in an engine control unit. They include several mathematical operations such as root square, exponential, division, that are time consuming for an embedded system to solve and thus the implementation may be a problem for a processor with limited computational resources. Because of these reasons, a new and simple method for the charge temperature predictions has been developed according to the invention. With the help of system identification techniques and vehicle test data, an empirical dynamic model for the charge temperature has been developed, based on physical concepts.

According to the invention, the charge temperature equation is given as: <maths><math overflow="scroll"><mtable><mtr><mtd><mtable><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><mrow><mrow><msub><mi>f</mi><mi>cv</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mi>N</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>EGR</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><mo>(</mo><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>-</mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mo>)</mo></mrow></mrow><mo>+</mo><mrow><mrow><msub><mi>f</mi><mi>cd</mi></msub><mo></mo><mrow><mo>(</mo><mrow><msub><mi>V</mi><mi>s</mi></msub><mo>,</mo><msub><mi>V</mi><mi>f</mi></msub><mo>,</mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mo>(</mo><mrow><msub><mi>T</mi><mi>o</mi></msub><mo>+</mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mo>)</mo></mrow></mrow><mo>+</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><mrow><mrow><msub><mi>f</mi><mi>cr</mi></msub><mo></mo><mrow><mo>(</mo><mrow><msub><mi>V</mi><mi>s</mi></msub><mo>,</mo><msub><mi>V</mi><mi>f</mi></msub><mo>,</mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mo>)</mo></mrow></mrow><mo></mo><msubsup><mi>T</mi><mi>ck</mi><mn>4</mn></msubsup></mrow><mo>+</mo><mrow><msub><mi>f</mi><mi>mr</mi></msub><mo></mo><msubsup><mi>T</mi><mi>mk</mi><mn>4</mn></msubsup></mrow></mrow></mrow></mtd></mtr></mtable></mtd><mtd><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mtd></mtr></mtable></math><img id="EMI-M00003" file="US06286366-20010911-M00003.TIF" img-content="math" img-format="tif" /><attachments><attachment idref="MATHEMATICA-00003" attachment-type="nb" file="US06286366-20010911-M00003.NB" /></attachments></maths>

The function f_cvin the first term of equation (3) provides the heat transfer contribution to the rate of charge temperature change dT_m/dt as the difference between the charge temperature T_mand the inlet air temperature T_inentering the manifold. This contribution is based on the engine speed N, the pressure P in the intake manifold and the exhaust gas recirculation (EGR) condition. The function F_cdin the second term of equation (3) provides the heat transfer contribution to the rate charge temperature change dT_m/dt as the difference of the engine coolant temperature T_cand the air inlet temperature T_in. This contribution is based on the vehicle speed V_s, the radiator fan on/off state V_fand the temperature of the engine coolant T_c. The function f_crin the third term of equation (3) provides the heat transfer contribution from heat radiation from the engine block based on the coolant temperature T_ck. This contribution is based on the vehicle speed V_s, the radiator fan on/off state V_fand the engine coolant temperature T_c. The function f_mrin the fourth term of equation (3) provides the radiation heat transfer effect from the manifold itself, where T_ckand T_mkare the absolute temperature of T_cand T_m, respectively.

Since the gas dynamic process is much faster than the heat transfer process, the engine speed N, the manifold pressure P and the EGR condition play the most significant roles in the quick response change of charge temperature T_m. The coolant temperature T_c, the inlet air temperature T_inand the vehicle speed V_swhich evolve in the intake manifold heat transfer process have a slow influence on the charge temperature. When the engine is hot, the radiative heat transfer is also not negligible.

Based on the theoretical models, the rate of intake charge temperature change dT_m/dt has now been defined as a function of related engine operation variables, as discussed above. For the practical implementation in the engine control unit, a discrete model of the difference equation (3) can then be defined as:

<maths><formula-text>T_m(n)=T_m(n−1)+f_cv[T_m(n−1)−T_in(n−1)]+f_cd[T_c(n−1)−T_in(n−1)]+f_crT_ck⁴(n−1)+f_mrT_mk⁴(n−<b>1)</b>  (4)</formula-text></maths>

where,

<maths><formula-text>f_cv=a₀+a₁N(n−1)+a₂N²(n−1)+a₃N³(n−1)+a₄N(n−1)P(n−1) +a₅R(n−1)+a₆P(n−1)R(n−1)+a₇P²(n−1)+a₈P³(n−1)R(n−1)</formula-text></maths>

<maths><formula-text>f_cdb₀+b₁V_s(n−1)+b₂V_n(n−1)+b₃V_f(n−1)</formula-text></maths>

<maths><formula-text>f_crC₀+C₁V_s(n−1)+C₂V_n(n−1)+C₃V_f(n−1)</formula-text></maths>

<maths><formula-text>V_n(n−1)=[α₀−T_c(n−1)][1−V_s(n−1)]if T_c(n−1)&lt;α₀; otherwise V_n(n−1)=0</formula-text></maths>

<maths><formula-text>T_ck(n−1)=β₀+β₁T_c(n−1)</formula-text></maths>

<maths><formula-text>T_mk(n−1)=β₀+β₁T_m(n−1)</formula-text></maths>

Here, n represents the current time and n−1 represents the previous time. The sampling time or the time interval between the executions is fixed. The current charge air temperature T_m(n) is calculated from the previous charge air temperature T_m(n−1), coolant temperature T_c(n−1), inlet air temperature T_in(n−1), vehicle speed V_s(n−1), fan on/off state V_f(n−1), engine speed N(n−1), manifold absolute pressure P(n−1), exhaust gas recirculation (EGR) duty cycle percentage R(n−1). Here, a₀. . . a₈, b₀. . . b₃, C₀. . . C₃, α₀, β₀and β₁are predetermined parameters and constants for a particular vehicle engine based on actual tests conducted on the engine at the development stage. Therefore, once these coefficients are determined for a particular vehicle, they are fixed for that vehicle to accurately determine the charge temperature T_m.

FIG. 2 shows a block diagram of a first order non-linear dynamic system <b>16</b> based on equations (3). The dynamic system <b>16</b> is separated into a feed forward portion <b>18</b> and a feedback portion <b>20</b>. In the feed forward portion <b>18</b>, the f_cdheat transfer contribution is determined by subtracting the inlet air temperature T_infrom the engine coolant temperature T_cin a summer <b>22</b>, and applying the difference to a function block <b>24</b> that determines f_cdbased on the vehicle speed V_s, the radiator fan on/off state V_f, and the coolant temperature T_c. To determine the heat transfer contribution from heat radiation from the engine block, the engine coolant temperature T_ckis multiplied to the fourth power in block <b>26</b>, and the coefficient function f_cris determined in block <b>28</b> based on the vehicle speed V_s, the radiator fan on/off state V_f, and the coolant temperature T_c.

In the feed forward portion <b>18</b>, to determine the heat contribution from the term f_cv, the inlet air temperature T_inis subtracted from the charge temperature Tm in a summer <b>30</b>, and f_cvis determined in block <b>32</b> based on the engine speed N, the manifold pressure P, and the EGR condition. To determine the contribution from the heat radiation from the intake manifold, the charge temperature T_mkis multiplied to the fourth power in block <b>34</b>, and f_mris then determined in block <b>36</b>. Each of the heat contribution from function blocks f_cd, f_cr, f_cvand f_mrare then added together in a summer <b>38</b>. This gives the change in charge temperature with respect to time dT_m/dt, which is integrated by an integrator <b>40</b> to generate the charge temperature T_m.

The technique for the parameter identification is to first define a prediction error function ε_i(q) in terms of the measured charge temperature {circumflex over (T)}_m(t_i)for N=1, . . . , N, and the predicted charge temperature T_in(t_i,q), for i=1, . . . , N, from the model including the parameter vector q=[a₀,a₁, . . . , a₈, b₁, . . . , b₃, c₀, c₁, . . . . c₃]. The error function is given as:

<maths><formula-text>ε_i(q)=T_m(t_i,q)−{circumflex over (T)}_m(t_i)  (5)</formula-text></maths>

Then, the parameters q are determined by minimizing the square error in all t_i, for i=1, . . . , N, as: <maths><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>min</mi><mo></mo><mstyle><mtext> </mtext></mstyle><mo></mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mo></mo><mrow><msubsup><mi>ε</mi><mi>i</mi><mn>2</mn></msubsup><mo></mo><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mtd></mtr></mtable></math><img id="EMI-M00004" file="US06286366-20010911-M00004.TIF" img-content="math" img-format="tif" /><attachments><attachment idref="MATHEMATICA-00004" attachment-type="nb" file="US06286366-20010911-M00004.NB" /></attachments></maths>

The procedure for determining the coefficients is illustrated in a flow diagram <b>46</b> shown in FIG. <b>3</b>. The charge temperature T_mand the model's input data are collected for training at box <b>48</b>. Then, initial values and coefficients for the particular vehicle are identified at box <b>50</b>. The parameters are downloaded to an engine controller for real time prediction as indicated by box <b>52</b>. The performance verification includes data collection for evaluation during the performance test, as indicated by box <b>54</b>. A decision diamond <b>56</b> determines if the coefficients accurately satisfy the charge temperature prediction based on the comparison with actual temperature measurements. If not, the process is performed again with new or modified coefficients.

When the engine is cool, the charge temperature T_mis equal to the inlet air temperature T_inIn the case of a hot restart, the charge temperature T_mis different from the inlet air temperature T_indue to the air flow pipe and manifold heating effect. Therefore, an estimation of initial charge temperature is required.

When the engine is off, there is no way to keep track of the charge temperature T_m. When the engine is turned on, the coolant temperature T_cand the inlet air temperature T_inare immediately available. These values are not enough to accurately determine the initial charge temperature T_m. In order to estimate the initial charge temperature T_m, the values of the coolant T_c, inlet air temperature T_inand predicted charge temperature T_mjust before the engine was turned off in the previous engine start are required. These values could be stored in a non volatile memory when the engine is shut off.

To obtain the initial value of the charge temperature T_mafter the engine is turned on, a set of engine-off differential equations are solved from the available information. To simplify the problem, the radiation effect is neglected in the engine-off model. Three unknowns, T_m, T_i, and t can be obtained by solving the following three equations. <maths><math overflow="scroll"><mtable><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mrow><mrow><msub><mi>f</mi><mn>11</mn></msub><mo></mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>12</mn></msub><mo></mo><msub><mi>T</mi><mi>i</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>13</mn></msub><mo></mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>14</mn></msub><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mrow><mrow><msub><mi>f</mi><mn>21</mn></msub><mo></mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>22</mn></msub><mo></mo><msub><mi>T</mi><mi>i</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>23</mn></msub><mo></mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>24</mn></msub><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mo></mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mrow><mo></mo><mi>t</mi></mrow></mfrac><mo>=</mo><mrow><mrow><msub><mi>f</mi><mn>31</mn></msub><mo></mo><msub><mi>T</mi><mi>c</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>32</mn></msub><mo></mo><msub><mi>T</mi><mi>i</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>33</mn></msub><mo></mo><msub><mi>T</mi><mi>in</mi></msub></mrow><mo>+</mo><mrow><msub><mi>f</mi><mn>34</mn></msub><mo></mo><msub><mi>T</mi><mi>m</mi></msub></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mtd></mtr></mtable></math><img id="EMI-M00005" file="US06286366-20010911-M00005.TIF" img-content="math" img-format="tif" /><attachments><attachment idref="MATHEMATICA-00005" attachment-type="nb" file="US06286366-20010911-M00005.NB" /></attachments></maths>

where T_iis the ambient temperature, t denotes time and f_ijare the constants which may be equal to zero when the coefficient is very small. Once the initial value is established, the estimation becomes a routine with each time step.

The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion, and from the accompanying drawings and claims, that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims.